One way and factorial anova
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One-Way and Factorial ANOVA. SPSS Lab #3. One-Way ANOVA. Two ways to run a one-way ANOVA Analyze  Compare Means  One-Way ANOVA Use if you have multiple DV’s, but only one IV Analyze  General Linear Model  Univariate Use if you have only one DV bc/ can provide effect size statistics

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One way anova
One-Way ANOVA

  • Two ways to run a one-way ANOVA

    • Analyze  Compare Means  One-Way ANOVA

      • Use if you have multiple DV’s, but only one IV

    • Analyze  General Linear Model  Univariate

      • Use if you have only one DV bc/ can provide effect size statistics

      • More on this later (factorial ANOVA section)


Method 1 compare means
Method #1: Compare Means

  • First we have to test if we meet the assumptions of ANOVA:

    • Independence of Observations

      • Cannot be tested statistically, is determined by research methodology only

    • Normally Distributed Data

      • Shapiro-Wilk’s W statistic, if significant, indicates significant non-normality in data

      • Analyze  Descriptive Statistics  Explore

        • Click on “Plots”, make sure “Normality Plots w/Tests” is checked



Testing assumptions1
Testing Assumptions

  • Homogeneity of Variances (Homoscedasticity)

    • Tested at the same time you test ANOVA

    • Analyze  Compare Means  One-Way ANOVA

      • Click on “Options” and make sure “Homogeneity of variance test” is checked

      • If violated, use Brown-Forsythe or Welch statistics, which do not assume homoscedasticity


Method 1 compare means1
Method #1: Compare Means

  • One-Way ANOVA

    • Analyze  Compare Means  One-Way ANOVA

    • “Dependent List” = DV’s; “Factor” = IV

    • Options

      • Descriptive

      • Fixed and random effects

      • Homogeneity of variance test

        • Levene’s Test: Significant result  Non-homogenous variances

      • Brown-Forsythe

      • Welch

      • Means plot




Method 1 compare means4
Method #1: Compare Means

  • One-Way ANOVA

    • Post-Hoc

      • Can only be done if your IV has 3+ levels

        • Pointless if only 2 levels, just look @ the means

      • Click the test you want, either with equal variances assumed or not assumed

      • DON’T just click all of them and see which one gives what you want (that’s cheating), select the test you want priori


Method 1 compare means5
Method #1: Compare Means

  • Contrasts

    • Click “Polynomial”, Leave “Degree” at default (“Linear”)

    • Enter in your coefficients

      • # of coefficients should equal # of levels of your IV

        • Doesn’t count missing cells, so if you have 3 levels, but no one in one of the levels, you should have 2 coefficients

      • Coefficients need to sum to 0


Method 1 compare means6
Method #1: Compare Means

  • Contrasts

    • Enter in your coefficients

      • IV = Race – 1=Caucasian, 2=African American, 3=Asian American, 4=Hispanic, 5=Native American, 6=Other, BUT there were no Native Americans in the sample

      • If you want to compare Caucasians to “Other”, coefficients = 1, 0, 0, 0, -1

      • Caucasians vs. everyone else = -1, .25, .25, .25, .25



Method 2 univariate
Method #2: Univariate

  • Univariate works for both one-way (1 IV) and factorial ANOVA’s (2+ IV’s)

  • Allows for specification of both fixed and random factors (IV’s)

  • Assumptions

    • Independence of Observations

    • Normally Distributed Data

      • Both same as one-way ANOVA


Factorial anova
Factorial ANOVA

  • Assumptions:

    • Homoscedasticity

      • Tested at the same time you test ANOVA

      • Click on Analyze  General Linear Model  Univariate

        • Click on “Options” and make sure “Homogeneity tests” is checked


Factorial anova1
Factorial ANOVA

  • Options

    • Estimated Marginal Means

      • Displays means, SD’s, & CI’s for each level of each IV selected

        • If “Compare main effects” is checked, works as one-way ANOVA on each IV selected

        • “Confidence interval adjustments” allows you to correct for inflation of alpha using Bonferroni or Sidak method

    • Descriptive statistics

    • Estimates of effect size

    • Observed power

      • Pointless, adds nothing to interpretation of p-value and e.s.

    • Homogeneity tests

      • Levene’s test



Factorial anova3
Factorial ANOVA

  • Save

    • Don’t worry about this for now

  • Post Hoc

    • Select the IV for which you wish to compare all levels against all other levels (i.e. that you don’t plan to do planned comparisons on)

    • Click on the right arrow button so the IV is in the box labeled “Post Hoc Tests for”

    • Check the post hoc tests you want done, either with equal variances assumed or not assumed

    • Click “Continue”


Factorial anova4
Factorial ANOVA

  • Plots

    • Horizontal Axis

      • What IV is on the x-axis

    • Separate Lines

    • Separate Plots


Factorial anova5
Factorial ANOVA

  • The following graph has the IV “Race” on the horizontal axis and separate lines by the IV “Gender”


Factorial anova6
Factorial ANOVA

  • Model

    • Allows you to:

      • Denote which main effects and interactions you are interested in testing (default is to test ALL of them)

      • Specify which type of sum of squares to use

    • Usually you won’t be tinkering with this


Factorial anova7
Factorial ANOVA

  • Contrasts

    • Tests all levels within one IV

    • Concern yourself with Simple only for now

    • “Reference category” = What level all others are compared to (either first or last, with this referring to how they were numbered)

    • Can test specific levels within one IV with specific levels in another IV, but requires knowledge of syntax



Factorial anova9
Factorial ANOVA

  • Interpreting interactions

    • See graphs